Reordering of complex SQL queries involving groupbys, joins, outer joins and full outer joins

Abstract

A method, apparatus, and article of manufacture for query simplification by applying generalized inference propagation and generalized transitive closure in SQL queries having selection, projection, join, outer join, and intersection operations. The disclosed transformations and enumeration method unify and solve the problems of 1) unnesting join aggregate queries, and 2) complete enumeration of queries containing outer joins, when the outer join predicate references an aggregated value, or the predicate references more than two base relations in a query subtree. The system first eliminates redundant sub-expressions and modifies expensive binary operations to inexpensive binary operations, then converts complex predicates to simple predicates by application of a generalized selection (GS) operator.

What is claimed is: 
     
       1. A method of simplifying a query performed by a computer to retrieve data from a relational database stored in a electronic storage device coupled to the computer, the method comprising the steps of: (a) eliminating redundant sub-expressions from the query and modifying expensive binary operations in the query to inexpensive binary operations, so that only simple and complex predicates remain in the query; and   (b) converting the complex predicates remaining in the query to simple predicates by application of a generalized selection (GS) operator.   
     
     
       2. The method of claim 1, further comprising the step of applying a simplification identity to a SELECT DISTINCT operator in the query. 
     
     
       3. The method of claim 1, further comprising the step of applying a simplification identity for a push-up of a GROUPBY operator in the query. 
     
     
       4. The method of claim 1, wherein the GS operator, σ *   p   r 2 , r 3  ! (r 1 ), of relation r 1  with respect to relations r 2  and r 3  comprises the relation (R 1 , V 1 , E'), wherein:   E'=σ.sub.p (r.sub.1){π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (r.sub.1)-π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (σ.sub.p (r.sub.1))} {π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (r.sub.1)-π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (σ.sub.p (r.sub.1))}     and wherein r 1  =(R 1 , V 1 , E 1 ), r 2  =(R 2 , V 2 , E 2 ), and r 3  =(R 3 , V 3 , E 3 ) comprise three relations such that R 2  .OR right.R 1 , R 3  .OR right.R 1 , R 2  ∩R 3  =.o slashed., V 2  .OR right.V 1 , V 3  .OR right.V 1 , and V 2  ∩V 3  =.o slashed., and p denotes a null-intolerant predicate in R 1 .   
     
     
       5. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU22## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       6. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU23## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       7. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU24##   where ⊙.di-elect cons.{→, ←, ⃡}wherein X.sub.i =(R.sub.i, V.sub.i, E.sub.i) are relational expressions for 1≦i≦3, and p.sub.i,j denote the predicates between expressions X.sub.i and X.sub.j.     
     
     
       8. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU25##   where ⊙.di-elect cons.{→, ←, ⃡}     wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j .   
     
     
       9. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU26## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       10. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU27## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       11. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU28## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       12. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU29## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       13. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU30## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       14. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU31## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       15. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU32## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       16. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU33## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       17. The method of claim 1, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU34## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       18. An apparatus for simplifying a query performed by a computer to retrieve data from a relational database stored in a electronic storage device, comprising: (a) means for eliminating redundant sub-expressions from the query and modifying expensive binary operations in the query to inexpensive binary operations, so that only simple and complex predicates remain in the query; and   (b) means for converting the complex predicates remaining in the query to simple predicates by application of a generalized selection (GS) operator.   
     
     
       19. The apparatus of claim 18, further comprising means for applying a simplification identity to a SELECT DISTINCT operator in the query. 
     
     
       20. The apparatus of claim 18, further comprising means for applying a simplification identity for a push-up of a GROUPBY operator in the query. 
     
     
       21. The apparatus of claim 18, wherein the GS operator, σ *   p   r 2 , r 3  ! (r 1 ), of relation r 1  with respect to relations r 2  and r 3  comprises the relation (R 1 , V 1 , E'), wherein:   E'=σ.sub.p (r.sub.1){π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (r.sub.1)-π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (σ.sub.p (r.sub.1))}{π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (r.sub.1)-π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (σ.sub.p (r.sub.1))}     and wherein r 1  =(R 1 , V 1 , E 1 ), r 2  =(R 2 , V 2 , E 2 ), and r 3  =(R 3 , V 3 , E 3 ) comprise three relations such that R 2  .OR right.R 1 , R 3  .OR right.R 1 , R 2  ∩R 3  =.o slashed., V 2  .OR right.V 1 , V 3  .OR right.V 1 , and V 2  ∩V 3  =.o slashed., and p denotes a null-intolerant predicate in R 1 .   
     
     
       22. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU35## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       23. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU36## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       24. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU37##   where ⊙.di-elect cons.{, →, ←, ⃡}wherein X.sub.i =(R.sub.i, V.sub.i, E.sub.i) are relational expressions for 1≦i≦3, and p.sub.i,j denote the predicates between expressions X.sub.i and X.sub.j.     
     
     
       25. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU38##   where ⊙.di-elect cons.{, →, ←, ⃡}wherein X.sub.i =(R.sub.i, V.sub.i, E.sub.i) are relational expressions for 1≦i≦3, and p.sub.i,j denote the predicates between expressions X.sub.i and X.sub.j.     
     
     
       26. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU39## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       27. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU40## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       28. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU41## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       29. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU42## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       30. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU43## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       31. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU44## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       32. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU45## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       33. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU46## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       34. The apparatus of claim 18, wherein the means for converting comprises means for applying a simplification expression to the query comprising: ##EQU47## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       35. An article of manufacture comprising a computer program carrier embodying one or more instructions of a method of simplifying a query performed by a computer to retrieve data from a relational database stored in a electronic storage device, the method comprising the steps of: (a) eliminating redundant sub-expressions from the query and modifying expensive binary operations in the query to inexpensive binary operations, so that only simple and complex predicates remain in the query; and   (b) converting the complex predicates remaining in the query to simple predicates by application of a generalized selection (GS) operator.   
     
     
       36. The article of manufacture of claim 35, wherein the method further comprises the step of applying a simplification identity to a SELECT DISTINCT operator in the query. 
     
     
       37. The article of manufacture of claim 35, wherein the method further comprises the step of applying a simplification identity for a push-up of a GROUPBY operator in the query. 
     
     
       38. The article of manufacture of claim 35, wherein the GS operator, σ *   p   r 2 , r 3  ! (r 1 ), of relation r 1  with respect to relations r 2  and r 3  comprises the relation (R 1 , V 1 , E'), wherein:   E'=σ.sub.p (r.sub.1){π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (r.sub.1)-π.sup.c.sub.R.sbsb.2.sub.V.sbsb.2 (σ.sub.p (r.sub.1))}{π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (r.sub.1)-π.sup.c.sub.R.sbsb.3.sub.V.sbsb.3 (σ.sub.p (r.sub.1))}     and wherein r 1  =(R 1 , V 1 , E 1 ), r 2  =(R 2 , V 2 , E 2 ), and r 3  =(R 3 , V 3 , E 3 ) comprise three relations such that R 2  .OR right.R 1 , R 3  .OR right.R 1 , R 2  ∩R 3  =.o slashed., V 2  .OR right.V 1 , V 3  .OR right.V 1 , and V 2  ∩V 3  =.o slashed., and p denotes a null-intolerant predicate in R 1 .   
     
     
       39. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU48## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       40. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU49## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       41. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU50##   where ⊙.di-elect cons.{, →, ←, ⃡}wherein X.sub.i =(R.sub.i, V.sub.i, E.sub.i) are relational expressions for 1≦i≦3, and p.sub.i,j denote the predicates between expressions X.sub.i and X.sub.j.     
     
     
       42. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU51##   where ⊙.di-elect cons.{, →, ←, ⃡}wherein X.sub.i =(R.sub.i, V.sub.i, E.sub.i) are relational expressions for 1≦i≦3, and p.sub.i,j denote the predicates between expressions X.sub.i and X.sub.j.     
     
     
       43. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU52## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       44. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU53## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       45. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU54## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       46. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU55## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       47. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU56## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       48. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU57## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       49. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU58## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       50. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU59## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j . 
     
     
       51. The article of manufacture of claim 35, wherein the converting step comprises the step of applying a simplification expression to the query comprising: ##EQU60## wherein X i  =(R i , V i , E i ) are relational expressions for 1≦i≦3, and p i ,j denote the predicates between expressions X i  and X j .